XmR Individuals Chart Formulas

The XmR (Individuals and Moving Range) chart can help you evaluate a process when there is only one measurement and they are farther apart: monthly postage expense and so on.

Here are the formulas used to calculate both the Moving Range and Individuals chart in QI Macros.

Moving Range Chart formula

moving range chart formula

Individuals X chart formula

individuals chart formula

k = number of data points

for n=2 observations (moving range is calculated from two samples, the present minus the previous value)

D4 = 3.267

D3 = 0

E2 = 2.660

Conforms with ANSI/ASQC B1, B2, B3 1996

QI Macros XmR Charts employ the Nelson Rule for Moving Range

"Any moving range (Ri) greater than 3.5*Rbar should be removed from the average moving range calculation."

In example below, point 20 (46.50) is greater than 3.5*11.14 (original Rbar), so it will be removed from Rbar Calculation which changes Rbar to 9.73 and UCL/LCL for both the X and R charts. 

Source: Control Charts for Individual Measurements, Lloyd S. Nelson, Journal of Quality Technology, Vol. 14, No. 34, July 1982.

Moving Range chart  example with Nelson range rules

Process: Calculate, plot, and evaluate the range chart first. If it is "out of control," so is the process. If the range chart looks okay, then calculate, plot, and evaluate the X chart.

Other Resources

The XmR Individuals chart is just one of the tools included in the QI Macros SPC Software for Excel.


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